<think>
Okay, I need to figure out how to answer the user's questions about the pathway enrichment analysis methods used in the provided scientific article. The user has given me an abstract and several sections from the paper, including the Methods section, Supporting Information, and other parts.

First, I'll go through each of the six questions one by one to gather as much information as possible.

1. **What tool was used for pathway enrichment analysis?**
   - Looking through the Methods and Supporting Info, especially S1 Fig which describes the RNA-seq pipeline, they mention using tools like Bowtie2, Tophat2, Cufflinks2, and Cuffdiff2. These are primarily for read alignment, transcript assembly, quantification, and differential expression analysis.
   - However, pathway enrichment typically requires different tools. The main text mentions GSEA (Gene Set Enrichment Analysis) in the Results section when discussing TCM and TEM-related genes. Also, S4 Fig explicitly talks about GSEA results for TCM and TEM gene sets.
   - So, the tool used is likely GSEA.

2. **Was a tool version number provided?**
   - The article doesn't mention any specific version numbers for GSEA or other tools related to pathway analysis. It only refers to general usage without specifying versions.

3. **What gene set library was queried (e.g., GO, KEGG, Reactome, or other)?**
   - In the Results and Discussion sections, they talk about TRM cells and genes associated with tissue residency, adhesion molecules, etc.
   - The GSEA in S4 Fig uses TCM and TEM-related gene sets. It doesn't specify if these are from GO, KEGG, etc., but since they're using custom or specific gene sets related to T cell memory, it's likely they used a specialized library rather than the standard GO or KEGG.

4. **Was a background gene list defined for pathway enrichment analysis?**
   - The article doesn't provide details on whether a specific background gene list was used. Typically, GSEA uses all genes as the background, but without explicit mention, it's unclear here.

5. **What statistical test was used for enrichment analysis?**
   - GSEA uses a permutation-based test to determine enrichment significance. However, the article doesn't specify this detail; it just mentions GSEA was performed without elaborating on the exact test.

6. **Was false discovery rate correction used to control the number of false positives in the pathway enrichment analysis?**
   - The Methods section and Supporting Info don't mention FDR correction explicitly for pathway analysis. While they do use FDR <0.05 for differential expression, there's no indication it was applied to GSEA results.

So, based on this analysis, I can structure the answers as follows:
</think>

| Question | Answer |
|----------|--------|
| 1. What tool was used for pathway enrichment analysis? | GSEA (Gene Set Enrichment Analysis) |
| 2. Was a tool version number provided? | Not described |
| 3. What gene set library was queried (e.g., GO, KEGG, Reactome or other)? | TCM and TEM-related gene sets (specific libraries not specified) |
| 4. Was a background gene list defined for pathway enrichment analysis? | Not described |
| 5. What statistical test was used for enrichment analysis? | Not described (but GSEA typically uses permutation-based tests) |
| 6. Was false discovery rate correction used to control the number of false positives in the pathway enrichment analysis? | Not described |

**Note:** The information provided is based on the content of the article and might not cover all details, as some aspects were not explicitly mentioned.